Journal
MATHEMATICAL PROGRAMMING
Volume 116, Issue 1-2, Pages 369-396Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-007-0120-x
Keywords
variational analysis and optimization; nonsmooth functions and set-valued mappings; generalized differentiation; marginal and value functions; mathematical programming
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In this paper we derive new results for computing and estimating the so-called Frechet and limiting (basic and singular) subgradients of marginal functions in real Banach spaces and specify these results for important classes of problems in parametric optimization with smooth and nonsmooth data. Then we employ them to establish new calculus rules of generalized differentiation as well as efficient conditions for Lipschitzian stability and optimality in nonlinear and nondifferentiable programming and for mathematical programs with equilibrium constraints. We compare the results derived via our dual-space approach with some known estimates and optimality conditions obtained mostly via primal-space developments.
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